[tsimionescu]

Yes, a is implied by b is equivalent to me to b implies a, and it is an atemporal relationship. This is how a lot of logic is taught and practiced, whether in mathematics, physics, engineering or programming. I am a programmer by trade, and even in programming most uses of logic have no concept of time.

When I say x + 1 = 7, therefore x = 6, I see the two statements as being true simultaneously, and simultaneously with the implication.

I am sure there exist logics where time is a necessary component of reasoning, and I am not downplaying their importance. But there also exist logics where time plays no part, and they are not more or less true.

[ukj]

The crux of the matter is information.

Symmetrical (equational) theories contain none.

Information mandates asymmetry.